A company produces two goods, X and Y. The profit function () of the company is given

A company produces two goods, X and Y. The profit function (Π) of the company is given as follows:

Π = 100 X – 2 X 2 – XY + 180 Y – 4 Y 2 The company is under obligation to produce a minimum combined output of X and Y equal to 30 units. Find the output of X and Y subject to a total of 30 units that maximize total profit by using both substitution and Lagrangian multiplier methods.